Question

By selling a product for Rs.1500, a person gets a profit of 20%. Find its cost price?

Answer 1

Hint: This type of question is based on the concept of percentage. We have to first assume the cost price to be x. given in the question 20% of x is the profit. But the total amount with the profit is 1500. On expressing an equation with variable x, we get \[x+\dfrac{20}{100}\times x=1500\]. Simplify the given equation by cancelling out the common terms. Take LCM and multiply the whole equation by 5 to find the value of x which is the cost price.

Complete step-by-step solution:
According to the question, we are asked to find the cost price of a product.
We have been given that on 20% of profit, the selling price is Rs.1500.
Let us assume the cost price to be x.
Therefore, the profit is 20 percent of x that is \[\dfrac{20}{100}\times x\].
On expressing the given situation into an expression, we get
SP=CP + profit
Here, SP is the selling price and CP is the cost price.
We know that SP=1500 and CP=x.
Therefore, we get
\[1500=x+\dfrac{20}{100}\times x\]
On further simplifying, we get
\[1500=x+\dfrac{20}{20\times 5}\times x\]
On cancelling out the common term 20 from the RHS, we get
\[1500=x+\dfrac{x}{5}\]
Now, take LCM in the right-hand side of the equation.
We get,
\[1500=\dfrac{5x+x}{5}\]
Multiply the whole equation by 5. We get
\[1500\times 5=\dfrac{5x+x}{5}\times 5\]
Cancelling out the common term 5 from the RHS, we get
\[1500\times 5=5x+x\]
On further simplification, we get
\[7500=6x\]
\[\Rightarrow 6x=7500\]
Now, divide the whole expression by 6.
\[\Rightarrow \dfrac{6x}{6}=\dfrac{7500}{6}\]
We can write 7500 as \[7500=1250\times 6\].
Therefore, we get
\[\Rightarrow \dfrac{6x}{6}=\dfrac{1250\times 6}{6}\]
Cancelling out the common term 6 from the numerator and denominator on both the sides of the expression, we get
\[x=1250\]
Therefore, the cost price of the product is Rs.1250.

Note: It is advisable to always assume x to be the cost price to solve this type of problem. Then form a linear equation with the variable x and find the value of x by doing necessary calculations. We should not subtract the profit from the cost price which will lead to a wrong answer. Avoid calculation mistakes based on sign conventions.